Question

An insurance company believes that people can be divided into two classes: those who are accident prone and those who are not. Their statistics show that an accident prone person will have an accident in a yearly period with probability $0.4$ whereas this probability is $0.2$ for the other kind. Given that $30\%$ of the people are accident prone, the probability that a new policy holder will have an accident within a year of purchasing a policy is

• A. $0.74$
• B. $0.26$
• C. $0.34$
• D. $0.66$

Answer 1

Answer: (B)

$0.26$

A new policy holder is either accident prone or not.
In case of 'accident prone', probability of having accident$=0.3\times 0.4=0.12$
In case of 'not accident prone', probability of having accident$=0.7\times 0.2=0.14$
Hence, total probability of a new policy holder having accident$=0.12+0.14=0.26$